Label |
Cremona label |
Class |
Cremona class |
Class size |
Class degree |
Conductor |
Discriminant |
Rank |
Torsion |
$\textrm{End}^0(E_{\overline\Q})$ |
CM |
Sato-Tate |
Semistable |
Potentially good |
Nonmax $\ell$ |
$\ell$-adic images |
mod-$\ell$ images |
Adelic level |
Adelic index |
Adelic genus |
Regulator |
$Ш_{\textrm{an}}$ |
Ш primes |
Integral points |
Modular degree |
Faltings height |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
1293.a1 |
1293e2 |
1293.a |
1293e |
$2$ |
$5$ |
\( 3 \cdot 431 \) |
\( 3^{3} \cdot 431^{5} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$5$ |
5.24.0.3 |
5B.1.2 |
$12930$ |
$48$ |
$1$ |
$0.336400665$ |
$1$ |
|
$0$ |
$16200$ |
$1.677980$ |
$155125609019771539456/401559694321077$ |
$[0, 1, 1, -111940, -14420480]$ |
\(y^2+y=x^3+x^2-111940x-14420480\) |
5.24.0-5.a.2.2, 2586.2.0.?, 12930.48.1.? |
$[(-787/2, 1289/2)]$ |
1293.a2 |
1293e1 |
1293.a |
1293e |
$2$ |
$5$ |
\( 3 \cdot 431 \) |
\( 3^{15} \cdot 431 \) |
$1$ |
$\Z/5\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$5$ |
5.24.0.1 |
5B.1.1 |
$12930$ |
$48$ |
$1$ |
$1.682003328$ |
$1$ |
|
$10$ |
$3240$ |
$0.873261$ |
$28589738658328576/6184378917$ |
$[0, 1, 1, -6370, 193540]$ |
\(y^2+y=x^3+x^2-6370x+193540\) |
5.24.0-5.a.1.2, 2586.2.0.?, 12930.48.1.? |
$[(44, 19)]$ |
1293.b1 |
1293b4 |
1293.b |
1293b |
$4$ |
$4$ |
\( 3 \cdot 431 \) |
\( 3^{3} \cdot 431 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
8.12.0.6 |
2B |
$10344$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1992$ |
$1.025059$ |
$26438903289204662017/11637$ |
$[1, 0, 0, -62064, 5946075]$ |
\(y^2+xy=x^3-62064x+5946075\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.1, 24.24.0-24.ba.1.12, $\ldots$ |
$[]$ |
1293.b2 |
1293b3 |
1293.b |
1293b |
$4$ |
$4$ |
\( 3 \cdot 431 \) |
\( 3^{3} \cdot 431^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.12.0.8 |
2B |
$10344$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1992$ |
$1.025059$ |
$7152577607925217/931693026267$ |
$[1, 0, 0, -4014, 85833]$ |
\(y^2+xy=x^3-4014x+85833\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 12.24.0-12.h.1.1, 3448.24.0.?, 10344.48.0.? |
$[]$ |
1293.b3 |
1293b2 |
1293.b |
1293b |
$4$ |
$4$ |
\( 3 \cdot 431 \) |
\( 3^{6} \cdot 431^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.12.0.1 |
2Cs |
$5172$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$996$ |
$0.678486$ |
$6454907876131057/135419769$ |
$[1, 0, 0, -3879, 92664]$ |
\(y^2+xy=x^3-3879x+92664\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.a.1.2, 1724.24.0.?, 5172.48.0.? |
$[]$ |
1293.b4 |
1293b1 |
1293.b |
1293b |
$4$ |
$4$ |
\( 3 \cdot 431 \) |
\( - 3^{12} \cdot 431 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.12.0.7 |
2B |
$10344$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$498$ |
$0.331913$ |
$-1417383186337/229051071$ |
$[1, 0, 0, -234, 1539]$ |
\(y^2+xy=x^3-234x+1539\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.ba.1.8, 862.6.0.?, 1724.24.0.?, $\ldots$ |
$[]$ |
1293.c1 |
1293a2 |
1293.c |
1293a |
$2$ |
$3$ |
\( 3 \cdot 431 \) |
\( 3 \cdot 431^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.2 |
3B.1.2 |
$2586$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$360$ |
$0.313351$ |
$799178752000/240188973$ |
$[0, 1, 1, -193, -782]$ |
\(y^2+y=x^3+x^2-193x-782\) |
3.8.0-3.a.1.1, 2586.16.0.? |
$[]$ |
1293.c2 |
1293a1 |
1293.c |
1293a |
$2$ |
$3$ |
\( 3 \cdot 431 \) |
\( 3^{3} \cdot 431 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$3$ |
3.8.0.1 |
3B.1.1 |
$2586$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$120$ |
$-0.235955$ |
$43614208000/11637$ |
$[0, 1, 1, -73, 217]$ |
\(y^2+y=x^3+x^2-73x+217\) |
3.8.0-3.a.1.2, 2586.16.0.? |
$[]$ |
1293.d1 |
1293d1 |
1293.d |
1293d |
$1$ |
$1$ |
\( 3 \cdot 431 \) |
\( - 3^{3} \cdot 431 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$5172$ |
$2$ |
$0$ |
$0.767643445$ |
$1$ |
|
$2$ |
$108$ |
$-0.525514$ |
$-10218313/11637$ |
$[1, 0, 1, -5, -7]$ |
\(y^2+xy+y=x^3-5x-7\) |
5172.2.0.? |
$[(3, 1)]$ |
1293.e1 |
1293c1 |
1293.e |
1293c |
$1$ |
$1$ |
\( 3 \cdot 431 \) |
\( 3 \cdot 431 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
$2586$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$136$ |
$-0.370501$ |
$12487168000/1293$ |
$[0, 1, 1, -48, 113]$ |
\(y^2+y=x^3+x^2-48x+113\) |
2586.2.0.? |
$[]$ |